Flavor changing neutral current (FCNC) processes, such as \(b\rightarrow s \ell ^+\ell ^-\) , give access to important tests of the standard model (SM) and searches for new physics beyond the SM.
Recently, some discrepancies with the SM are reported in several observables in \(B\)  meson decays, for example, the angular-distribution
observable \(P^{\prime }_5\)  of \(B^0\rightarrow K^{*0}\mu ^+\mu ^-\)  [1]}, [2]}, [3]}, [4]} and the lepton flavor universality observables \(R_{K^+}\)  and \(R_{K^{*0}}\)  with \(R_M=\frac{\mathcal {B}(B\rightarrow M\mu ^+\mu ^-)}{\mathcal {B}(B\rightarrow Me^+e^-)}\)  [5]}, [6]}.
Semileptonic baryon decays are quite different to \(B,D,K\)  meson ones, for instance, the initial baryons
may be polarized, the transitions involve a diquark system as a spectator
rather than a single-quark, and the \(W\) -exchange contributions
of two-quark and three-quark transitions might appear in baryon decays. Therefore, the baryon
decays provide the important additional tests of the SM predictions, which can be used to improve the understanding of recent anomalies in
\(B\)  meson decays. Recently significant experimental progress has been achieved in studying rare \(\Lambda _b\)  decays.
The \(\Lambda _b\rightarrow \Lambda \mu ^+\mu ^-\)  baryon decay is the only one measured among the \(T_{b3}\rightarrow T_8\ell ^+\ell ^-\)  decays at present. \(\mathcal {B}(\Lambda _b\rightarrow \Lambda \mu ^+\mu ^-)\)  was first measured by the CDF Collaboration [7]} and then greatly improved by LHCb [8]}, [9]}. For \(T_{c3}\rightarrow T_8\ell ^+\ell ^-\)  decays, only \(\mathcal {B}(\Lambda _c\rightarrow pe^+e^-)\)  and \(\mathcal {B}(\Lambda _c\rightarrow p\mu ^+\mu ^-)\)  have been upper limited by \(BABAR\)  and LHCb [10]}, [11]}. As for \(T_8\rightarrow T^{\prime }_8\ell ^+\ell ^-\)  decays, \(\Xi ^0\rightarrow \Lambda ^0 e^+e^-\)  and \(\Sigma ^+\rightarrow p\mu ^+\mu ^-\)  have been measured by NA48
[12]} and HyperCP [13]}, respectively.
With the experiment development,
some \(\mathcal {B}_1\rightarrow \mathcal {B}_2\ell ^+\ell ^-\)  decays will be improved or detected by the BESIII, LHCb, and Belle-II Collaborations in the near future, so
it is necessary to study \(\mathcal {B}_1\rightarrow \mathcal {B}_2\ell ^+\ell ^-\)  decays theoretically.
